Speaker of the House John Boehner, R-Ohio, speaks after a meeting with President Obama at the White House. / Win McNamee, Getty Images

by Gregory Korte, Catalina Camia and Aamer Madhani, USA TODAY

by Gregory Korte, Catalina Camia and Aamer Madhani, USA TODAY

WASHINGTON - President Obama and House Republicans, battling over who was at fault for the four-day partial shutdown of the federal government, found one point they could agree on Friday:

Federal workers sent home during the shutdown should get back pay when the government reopens.

The Republican-controlled House is set to vote on the Federal Employee Retroactive Pay Fairness Act Saturday. The Obama Administration, which had opposed piecemeal bills to resolve the shutdown, said Friday it "strongly supports" the measure.

"The Administration appreciates that the Congress is acting promptly to move this bipartisan legislation and looks forward to the bill's swift passage," the Office of Management and Budget said in a statement. "This bill alone, however, will not address the serious consequences of the funding lapse, nor will a piecemeal approach to appropriations bills."

That agreement leaves only the Senate to decide whether to approve back pay. "I don't know anything about what the House is planning to do," said Senate Majority Leader Harry Reid, D-Nev., complaining about the flurry of Republican bills with different demands and piecemeal approaches. He said the Senate would be in session Saturday to deal with whatever the House sent over.

The agreement was a rare moment of accord in an otherwise intractable standoff over government spending, the Affordable Care Act and the debt limit. The two sides traded shots Friday over which side was responsible for the shutdown, which began Tuesday after Congress failed to pass a spending bill for the new fiscal year.

"This isn't some damn game," Speaker John Boehner said after a GOP conference meeting. He slammed down a copy of the Wall Street Journal, where an anonymous senior White House official was quoted as saying Obama was "winning" the shutdown.

"The American people don't want their government shut down and neither do I. All we're asking for is to sit down and have a discussion ... to reopen the government and bring fairness to the American people under Obamacare," Boehner said.

"There's no winning," Obama said on a lunchtime visit to a Pennsylvania Avenue sandwich shop with Vice President Biden. "No one is winning."

Obama said the shutdown "could be over today."

"I'm happy to have negotiations but we can't do it with a gun held to the head of the American people," he said. Obama and congressional Democrats say they will negotiate on a broad, long-term budget deal after Republicans agree to end the shutdown and raise the debt ceiling.

The unnamed White House official quoted said essentially the same thing that Republican Sen. Rand Paul of Kentucky was overheard telling his Kentucky colleague, Senate Minority Leader Mitch McConnell, on a live microphone Thursday: "We're going to win this, I think."

As the shutdown ends its first work week, the impasse is beginning to do damage to the economy, economists said.

Moody's economist Mark Zandi said the first week of the shutdown has already shaved one or two decimal points off his estimate of 2.5% economic growth in the fourth quarter. A two-week shutdown would reduce growth to 2%, and a three-week shutdown would bring it to 1.6%

"If it goes on for a month, then growth will be closer to 1%, which I would characterize as pretty close to stall speed," Zandi said.

That assumes the debt limit is increased by Oct. 17 -- the date by which Treasury Secretary Jacob Lew says the government will run out of borrowed money. If Congress doesn't raise the $16.7 trillion debt limit, the United States would face its first-ever default.

"Let me be clear: If we breached the debt limit -- I think the the right word would be 'catastrophic' -- for the economy," Zandi said.

Rep. Jeb Hensarling, R-Texas, said that doesn't have to happen. The chairman of the House Financial Services Committee said Treasury should prioritize payments on debt and Social Security, and accused Obama of trying to "spook the markets."

But in an interview taped Friday for C-SPAN's Newsmakers, he also emphatically denied market-calming reports that Boehner would seek Democratic votes to raise the debt limit.

The House voted Friday on bills that would provide short-term funding for disaster relief and a program that provides food aid to women and children. Democrats have consistently rejected a piecemeal approach, and tried a number of procedural ploys Friday to force a vote on a "clean": continuing resolution to fund the government through Nov. 15.

"It will take some coming together on the Republican side," House Minority Leader Nancy Pelosi, D-Calif., said in a CBS News interview. "It's very hard to negotiate with the Republicans when they can't negotiate with themselves."

While Obama supports retroactive pay, the White House said he would veto the short-term measures. "Consideration of appropriations bills in this fashion is not a serious or responsible way to run the United States government," the OMB policy statement said. "Instead of opening up a few government functions, the House of Representatives should reopen all of the government."

Republicans accused the president of having "interesting priorities."

"So, to recap, the President signed the troop funding bill, and does not oppose back-pay, but he has promised to veto bills helping veterans, cancer research, National Parks, the District of Columbia," said House Speaker John Boehner's spokesman Michael Steel.

"I would have to say it takes a big worry off my mind," said Cindy Blythe, a Coast Guard management analyst in Topeka, Kan. " It's an aggravation that we're furloughed because Cong couldn't get it together. They had an entire year to get this done. This is not something that came out of the blue."